Kovacs, Balazs and Li, Buyang (2023) Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems. IMA JOURNAL OF NUMERICAL ANALYSIS, 43 (4). pp. 1937-1969. ISSN 0272-4979, 1464-3642
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Maximal parabolic L-p-regularity of linear parabolic equations on an evolving surface is shown by pulling back the problem to the initial surface and studying the maximal L-p-regularity on a fixed surface. By freezing the coefficients in the parabolic equations at a fixed time and utilizing a perturbation argument around the freezed time, it is shown that backward difference time discretizations of linear parabolic equations on an evolving surface along characteristic trajectories can preserve maximal L-p-regularity in the discrete setting. The result is applied to prove the stability and convergence of time discretizations of nonlinear parabolic equations on an evolving surface, with linearly implicit backward differentiation formulae characteristic trajectories of the surface, for general locally Lipschitz nonlinearities. The discrete maximal L-p-regularity is used to prove the boundedness and stability of numerical solutions in the L-infinity(0, T; W-1,W-infinity) norm, which is used to bound the nonlinear terms in the stability analysis. Optimal-order error estimates of time discretizations in the L-infinity(0, T; W-1,W-infinity) norm is obtained by combining the stability analysis with the consistency estimates.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FINITE-ELEMENT-METHOD; PARABOLIC PDES; DIFFUSION; EQUATIONS; ALGORITHM; FLOW; FEM; APPROXIMATIONS; CONVERGENCE; DRIVEN; evolving surface; nonlinear parabolic equations; locally Lipschitz continuous; backward differentiation formulae; linearly implicit; maximal L-p-regularity; stability; convergence; maximum norm |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Petra Gürster |
| Date Deposited: | 01 Sep 2023 08:51 |
| Last Modified: | 01 Sep 2023 08:51 |
| URI: | https://pred.uni-regensburg.de/id/eprint/57186 |
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